Nye’s tensor versus its scalar and vector measures in the quantification of geometrically necessary dislocations by EBSD

EBSD orientation data are widely employed to evaluate the crystal curvature (orientation gradient) and, consequently, derive Nye’s tensor indicative of geometrically necessary dislocations (GND). These defects attract a vivid interest because of their contributions to the strain-induced microstructure and the work hardening. The GND density is usually derived from either the measured Nye’s tensor itself or its appropriate scalar measures scaled by the Burgers vector magnitude of lattice dislocations. Besides, the net Burgers vector of GND crossing a unit area of the specimen section can be employed to assess a lower bound for the GND density. Based on various presumptions, these approaches differ in their advantages and limitations, which should be kept in mind in specific applications. Along with estimates for distributions and average densities of GND, the paper particularly focuses on a method to identify by EBSD their constituent Burgers vectors. This research makes use of EBSD data on dissimilar states of copper with allowance for important issues that have not attracted due regard so far. They are dependences of results on the step size and a way to differentiate discrete orientation data.